Moderate Deviation Principle for dynamical systems with small random perturbation

Details Moderate Deviation Principle for dynamical systems with small random perturbation Moderate Deviation Principle for dynamical systems with small random perturbation

2011-07-18

arxiv.org/abs/1107.3432v1

Mathematics

Probability

Scientific paper

Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d where $b:\rr^d\rightarrow\rr^d$ is $C^1$ such that $ \leq C(1+|x|^2)$, $\sigma:\rr^d\rightarrow \MM(d\times n)$ is locally Lipschitzian with linear growth, and $B_t$ is a standard Brownian motion taking values in $\rr^n$. Freidlin-Wentzell's theorem gives the large deviation principle for $X^\e$ for small $\e$. In this paper we establish its moderate deviation principle.

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